Question

What is the value today of a money machine that will pay $2,123.00 per year for 8.00 years? Assume the first payment is made today and that there are 8.0 total payments. The interest rate is 6.00%.

Answer 1

Present value of investment is calculated as: P= F/(1+r)^t; where F is Future value of the investment, P is Present value of the investment, r is the annual interest rate and t is the number of years

From the given information, value today is 2123+2123/1.06+2123/1.06^2+...2123/1.06^7.

The cashflows from 2 to 8 can be considered as annuity.

Present value of annuity is calculated as C*(1-(1+r)^-n)/r; where C is the annual cashflow, r is the discount rate and n is the number of years.

So, Value today= 2123+2123*(1-1.06^-7)/6%

= 13974.40.

So, the value today of the money machine= $13974.40